A Public Key Cryptosystem Based on Non-abelian Finite Groups
We present a new approach to designing public-key cryptosystems based on covers and logarithmic signatures of non-abelian finite groups. Initially, we describe a generic version of the system for a large class of groups. We then propose a class of 2-groups and argue heuristically about the system’s...
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| Published in | Journal of cryptology Vol. 22; no. 1; pp. 62 - 74 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer-Verlag
01.01.2009
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0933-2790 1432-1378 1432-1378 |
| DOI | 10.1007/s00145-008-9033-y |
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| Abstract | We present a new approach to designing public-key cryptosystems based on covers and logarithmic signatures of non-abelian finite groups. Initially, we describe a generic version of the system for a large class of groups. We then propose a class of 2-groups and argue heuristically about the system’s security. The system is scalable, and the proposed underlying group, represented as a matrix group, affords significant space and time efficiency. |
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| AbstractList | We present a new approach to designing public-key cryptosystems based on covers and logarithmic signatures of non-abelian finite groups. Initially, we describe a generic version of the system for a large class of groups. We then propose a class of 2-groups and argue heuristically about the system’s security. The system is scalable, and the proposed underlying group, represented as a matrix group, affords significant space and time efficiency. |
| Author | Magliveras, Spyros S. van Tran, Trung Lempken, Wolfgang Wei, Wandi |
| Author_xml | – sequence: 1 givenname: Wolfgang surname: Lempken fullname: Lempken, Wolfgang organization: Institut für Experimentelle Mathematik, Universität Duisburg-Essen – sequence: 2 givenname: Trung surname: van Tran fullname: van Tran, Trung organization: Institut für Experimentelle Mathematik, Universität Duisburg-Essen – sequence: 3 givenname: Spyros S. surname: Magliveras fullname: Magliveras, Spyros S. email: spyros@fau.edu organization: Department of Mathematical Sciences, Center for Cryptology and Information Security, Florida Atlantic University – sequence: 4 givenname: Wandi surname: Wei fullname: Wei, Wandi organization: Department of Mathematical Sciences, Center for Cryptology and Information Security, Florida Atlantic University |
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| Cites_doi | 10.1137/S0097539795293172 10.1007/s00145-001-0018-3 10.1007/BF02451113 10.1109/TIT.1985.1057074 10.1007/978-3-642-64981-3 10.1215/ijm/1255637483 |
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| Keywords | Uniform cover Trapdoor one-way function Suzuki 2-group Logarithmic signature Public-key cryptosystem Performance evaluation Scalability Abelian group Space time Finite group Security of data Digital signature Public key cryptography Backdoor Uniform cover. Trapdoor one-way function Suzuki 2-group |
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| References | Magliveras, Memon (CR6) 1992; 5 Huppert, Blackburn (CR4) 1982 Shor (CR9) 1997; 26 Magliveras (CR5) 1986 Huppert (CR3) 1967 CR8 ElGamal (CR1) 1985; 31 Magliveras, Stinson, van Trung (CR7) 2002; 15 Higman (CR2) 1963; 7 9033_CR8 S.S. Magliveras (9033_CR6) 1992; 5 G. Higman (9033_CR2) 1963; 7 S.S. Magliveras (9033_CR7) 2002; 15 B. Huppert (9033_CR3) 1967 B. Huppert (9033_CR4) 1982 S.S. Magliveras (9033_CR5) 1986 T. ElGamal (9033_CR1) 1985; 31 P. Shor (9033_CR9) 1997; 26 |
| References_xml | – year: 1982 ident: CR4 publication-title: Finite Groups II – volume: 26 start-page: 1484 issue: 5 year: 1997 end-page: 1509 ident: CR9 article-title: Polynomial time algorithms for prime factorization and discrete logarithms on quantum computers publication-title: SIAM J. Comput. doi: 10.1137/S0097539795293172 – volume: 15 start-page: 285 year: 2002 end-page: 297 ident: CR7 article-title: New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups publication-title: J. Cryptol. doi: 10.1007/s00145-001-0018-3 – ident: CR8 – volume: 7 start-page: 79 year: 1963 end-page: 96 ident: CR2 article-title: Suzuki 2-groups publication-title: Ill. J. Math. – start-page: 972 year: 1986 end-page: 975 ident: CR5 article-title: A cryptosystem from logarithmic signatures of finite groups publication-title: Proceedings of the 29th Midwest Symposium on Circuits and Systems – year: 1967 ident: CR3 publication-title: Endliche Gruppen I – volume: 5 start-page: 167 year: 1992 end-page: 183 ident: CR6 article-title: The algebraic properties of cryptosystem PGM publication-title: J. Cryptol. doi: 10.1007/BF02451113 – volume: 31 start-page: 469 year: 1985 end-page: 472 ident: CR1 article-title: A public key cryptosystem and a signature scheme based on discrete logarithms publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.1985.1057074 – volume-title: Endliche Gruppen I year: 1967 ident: 9033_CR3 doi: 10.1007/978-3-642-64981-3 – volume: 31 start-page: 469 year: 1985 ident: 9033_CR1 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.1985.1057074 – volume: 26 start-page: 1484 issue: 5 year: 1997 ident: 9033_CR9 publication-title: SIAM J. Comput. doi: 10.1137/S0097539795293172 – volume-title: Finite Groups II year: 1982 ident: 9033_CR4 – start-page: 972 volume-title: Proceedings of the 29th Midwest Symposium on Circuits and Systems year: 1986 ident: 9033_CR5 – volume: 15 start-page: 285 year: 2002 ident: 9033_CR7 publication-title: J. Cryptol. doi: 10.1007/s00145-001-0018-3 – ident: 9033_CR8 – volume: 5 start-page: 167 year: 1992 ident: 9033_CR6 publication-title: J. Cryptol. doi: 10.1007/BF02451113 – volume: 7 start-page: 79 year: 1963 ident: 9033_CR2 publication-title: Ill. J. Math. doi: 10.1215/ijm/1255637483 |
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| SubjectTerms | Applied sciences Coding and Information Theory Combinatorics Communications Engineering Computational Mathematics and Numerical Analysis Computer Science Computer systems Cryptography Exact sciences and technology Information, signal and communications theory Networks Probability Theory and Stochastic Processes Signal and communications theory Telecommunications and information theory |
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| Title | A Public Key Cryptosystem Based on Non-abelian Finite Groups |
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